need help with all of this question...a worked solution would be really helpful

7. A bag contains 4 red and 2 blue balls, all of the same size. A ball is selected at random and removed from the bag. This is repeated until a blue ball is pulled out of the bag.
The random variable B is the number of balls that have been removed from the bag.
(a) Show that P(B = 2) = 4/15 . (2 marks)
(b) Find the probability distribution of B. (4 marks)
(c) Find E(B). (3 marks)
The bag and the same 6 balls are used in a game at a funfair. One ball is removed from the bag at a time and a contestant wins 50 pence if one of the first two balls picked out is blue.
(d) What are the expected winnings from playing this game once? (4 marks)
For £1, a contestant gets to play the game three times.
(e) What is the expected profit or loss from the three games? (3 marks)

I get you draw a tree diagram but how many trails? 2? I got part a) right but I don't know how ... can someone send me a worked solution please?

(Original post by N123456789)
need help with all of this question...a worked solution would be really helpful

7. A bag contains 4 red and 2 blue balls, all of the same size. A ball is selected at random and removed from the bag. This is repeated until a blue ball is pulled out of the bag.
The random variable B is the number of balls that have been removed from the bag.
(a) Show that P(B = 2) = 4/15 . (2 marks)
(b) Find the probability distribution of B. (4 marks)
(c) Find E(B). (3 marks)
The bag and the same 6 balls are used in a game at a funfair. One ball is removed from the bag at a time and a contestant wins 50 pence if one of the first two balls picked out is blue.
(d) What are the expected winnings from playing this game once? (4 marks)
For £1, a contestant gets to play the game three times.
(e) What is the expected profit or loss from the three games? (3 marks)

I get you draw a tree diagram but how many trails? 2? I got part a) right but I don't know how ... can someone send me a worked solution please?

What have you tried? You've got a right but you don't know how, I think you do know how but you've just got confused along the way. How did you calculate P(B=2)? For the probability distribution you could find all the values that B takes and their probabilities in a very similar fashion to P(B=2).

(Original post by N123456789)
for part a) I just multiplied along the branches of tree diagram and used trial and improvement to get the first answer now that I remember

Okay, trial and improvement got you there. So why was it 2/3 * 2/5? Can you interpret this result to understand how you would do it if you weren't given the answer, and so find the answers for the other values of B?

(please quote me if you are replying so I can see that you have replied )

(Original post by SeanFM)
Okay, trial and improvement got you there. So why was it 2/3 * 2/5? Can you interpret this result to understand how you would do it if you weren't given the answer, and so find the answers for the other values of B?

(please quote me if you are replying so I can see that you have replied )

Spoiler:

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how did you get 2/3 and 2/5? on my tree diagram I got 2/6 x 4/5. I have no idea what I'm doing I would send an imagine of what ive done but it won't send